Scabies. When you say "mange", you are referring to the scabiesmite. This mite is highly contagious. You are susceptible to getting infested with this with any contact with the skin or clothing of this person. You should notify your supervisor of the situation and have them help to deal with this. This is a public health issue. If you contract this, you can be treated. Symptoms can last for a while.

Mange. Mange is a term used only or mostly for animals. It is a type of dermatitis associated to skin parasites like the one in humans called scabies ( sarcoptes aescaviaei). These are very pruriginous ( itchy) skin lesions and yes, that may be transmitted in contact with clothes, bed sheets, personal close contact with skin.